Buses depart frequently for Damascus, Homs, and Deir-az-Zur.The bus station is a little under a kilometre away from the main street, so do not pay anymore than 50 Syrian Pounds for a taxi with your luggage. For other destinations, you may need a private car.
If hiring a private car, you might want to consider side trips to Qasr al-Heir ash-Sharki - a partially excavated Ummayad palace quite literally in the middle of nowhere - and Rasafa, originally a Roman city with heavy Byzantine influence, also used by the Ummayads before being destroyed in the Abbasid era. Rasafa is also of interest for the stone it's built out of, more a quartz-like crystal instead of the usual granite or sandstone. Makes for a unique appearance. This route takes you quite close to the Euphrates, and you can be dropped off in Raqqa, Aleppo, or Hama. Car hire can be price, and the driver still has to get back to Palmyra. Private tours are the real money maker in the Syrian tourism industry, so expect to pay as much as S5000 US$100, if you're heading for Aleppo or Hama. A bit less to Raqqa.
